Bài 1: Giải các phương trình dưới đây
1) x2 - 9 = (x - 3)(5x +2)
2) x3 - 1 = (x - 1)(x2 - 2x +16)
3) 4x2 (x - 1) - x + 1 = 0
4) x3 + 4x2 - 9x - 36 = 0
5) (3x + 5)2 = (x - 1)2
6) 9 (2x + 1)2 = 4 (x - 5)2
7) x2 + 2x = 15
8) x4 + 5x3 + 4x2 = 0
9) (x2 - 4) - (x - 2)(3 - 2x) = 0
10) (3x + 2)(x2 - 1) = (9x2 - 4) (x + 1)
11) (3x - 1)(x2 + 2) = (3x - 1)(7x - 10)
12) (2x2 + 1) (4x - 3) = (x - 12)(2x2 + 1)
1: \(\Leftrightarrow\left(x-3\right)\left(x+3\right)-\left(x-3\right)\left(5x+2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(-4x+1\right)=0\)
hay \(x\in\left\{3;\dfrac{1}{4}\right\}\)
2: \(\Leftrightarrow\left(x-1\right)\left(x^2+x+1\right)-\left(x-1\right)\left(x^2-2x+16\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x+1-x^2+2x-16\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x-15\right)=0\)
hay \(x\in\left\{1;5\right\}\)
3: \(\Leftrightarrow\left(x-1\right)\left(4x^2-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(2x-1\right)\left(2x+1\right)=0\)
hay \(x\in\left\{1;\dfrac{1}{2};-\dfrac{1}{2}\right\}\)
4: \(\Leftrightarrow x^2\left(x+4\right)-9\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x-3\right)\left(x+3\right)=0\)
hay \(x\in\left\{-4;3;-3\right\}\)
5: \(\Leftrightarrow\left[{}\begin{matrix}3x+5=x-1\\3x+5=1-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-6\\4x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-1\end{matrix}\right.\)
6: \(\Leftrightarrow\left(6x+3\right)^2-\left(2x-10\right)^2=0\)
\(\Leftrightarrow\left(6x+3-2x+10\right)\left(6x+3+2x-10\right)=0\)
\(\Leftrightarrow\left(4x+13\right)\left(8x-7\right)=0\)
hay \(x\in\left\{-\dfrac{13}{4};\dfrac{7}{8}\right\}\)
1.
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)=\left(x-3\right)\left(5x-2\right)\)
\(\Leftrightarrow x+3=5x-2\)
\(\Leftrightarrow4x=5\Leftrightarrow x=\dfrac{5}{4}\)
2.
\(\Leftrightarrow\left(x-1\right)\left(x^2+x+1\right)=\left(x-1\right)\left(x^2-2x+16\right)\)
\(\Leftrightarrow x^2+x+1=x^2-2x+16\)
\(\Leftrightarrow3x=15\Leftrightarrow x=5\)
3.
\(\Leftrightarrow4x^2\left(x-1\right)-\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(4x^2-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{2};x=-\dfrac{1}{2}\end{matrix}\right.\)
7.
\(\Leftrightarrow x^2+2x-15=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)
8.\(\Leftrightarrow x^4+x^3+4x^3+4x^2=0\)
\(\Leftrightarrow x^3\left(x+1\right)+4x^2\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^3+4x^2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=0;x=-4\end{matrix}\right.\)
9.\(\Leftrightarrow\left(x-2\right)\left(x+2\right)=\left(x-2\right)\left(3-2x\right)\)
\(\Leftrightarrow x+2=3-2x\)
\(\Leftrightarrow3x=1\Leftrightarrow x=\dfrac{1}{3}\)
Em tách nhỏ bài ra để các bạn làm đỡ ngán nha!
1)
\(x^2-9=\left(x-3\right).\left(5x+2\right)\\ \Leftrightarrow\left(x-3\right).\left(x+3\right)=\left(x-3\right).\left(5x+2\right)\\ \Leftrightarrow\left(x-3\right).\left(x+3-5x-2\right)=0\\ \Leftrightarrow\left(x-3\right).\left(-4x+1\right)=0\\ \Leftrightarrow\left(x-3\right)=0.or\left(-4x+1\right)=0\\ \Leftrightarrow x=3.or.x=-\dfrac{1}{4}\\ \Rightarrow S=\left\{3;-\dfrac{1}{4}\right\}\)
2)
\(x^3-1=\left(x-1\right).\left(x^2-2x+16\right)\\ \Leftrightarrow\left(x-1\right).\left(x^2+x+1\right)=\left(x-1\right).\left(x^2-2x+16\right)\\ \Leftrightarrow\left(x-1\right).\left(x^2+x+1-x^2+2x-16\right)=0\\ \Leftrightarrow\left(x-1\right).\left(3x-15\right)=0\\ \Leftrightarrow3.\left(x-1\right).\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-5=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=5\end{matrix}\right.\\ \Rightarrow S=\left\{1;5\right\}\)
3)
\(4x^2.\left(x-1\right)-x+1=0\\ \Leftrightarrow4x^2.\left(x-1\right)-\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right).\left(4x^2-1\right)=0\\ \Leftrightarrow\left(x-1\right).\left(2x+1\right).\left(2x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x+1=0\\2x-1=0\\x-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=\dfrac{1}{2}\\x=1\end{matrix}\right.\\ \Rightarrow S=\left\{\pm\dfrac{1}{2};1\right\}\)
10.\(\Leftrightarrow\left(3x+2\right)\left(x-1\right)\left(x+1\right)=\left(3x-2\right)\left(3x+2\right)\left(x+1\right)\)
\(\Leftrightarrow x-1=3x-2\)
\(\Leftrightarrow2x=1\Leftrightarrow x=\dfrac{1}{2}\)
11.\(\Leftrightarrow x^2+2=7x-10\)
\(\Leftrightarrow x^2-7x+12=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=3\end{matrix}\right.\)
12.\(\Leftrightarrow4x-3=x-12\)
\(\Leftrightarrow3x=-9\Leftrightarrow x=-3\)
